Problem 3. Yet another previous midterm exam problem. Consider the responses shown in Figure 2 from four PI controllers applied to a laboratory heat exchanger. When evaluated in simulation using MATLAB w/Simulink on a nominal plant model (generated from inflection point analysis on a process reaction curve), all four control systems resulted in stable closed- loop responses, although with varying performance characteristics. DEFAULT 2 HOURS HM HM HM HM VORSTR Cont. C HTEX5 HEAT EXCHANGER Cont. A 100 Cont. B y and r Cont. D 75 50 25 u d 10/19/00 17:36:25 MIN 0 120 105 90 75 60 45 AAA PO Figure 2: Heat exchanger response for various PI controllers real-life data! The signals in Figure 2 are from a real-time display of a Honeywell TPS system, interfaced to the heat exchanger. These correspond to the outlet tube temperature and its setpoint (y and r, top curve), steam valve position (u, middle curve) and inlet tube flowrate (d, bottom curve). The closed-loop responses for controllers A and B correspond to setpoint tracking scenarios, while those for controllers C and D correspond to disturbance rejection. a) Which of the two setpoint tracking controllers would you consider to be best from the standpoint of minimizing a norm criterion on the control error ec, such as the Integral Square Error (ISE) or Integral Absolute Error (IAE)? Justify your response. b) Which of the four closed-loop responses would you say is the best from the standpoint of shape and character of response (considering both controlled and manipulated vari- ables)? Explain your reasoning for the best case, and indicate one problematic issue you see in the responses for the other three. c) Which closed-loop system would you say is the least robust (i.e., it appears most sensitive to model uncertainty)? Explain.